# Anova residuals

Hi Karen – thanks for the article. This can be a confusing topic. Say I have a categorical variable with three levels (. country) and I am using it to predict income. After using a General Linear Model to get residuals I check to see if they were normally distributed using a Shapiro-Wilk test. As a whole the residuals were normally distributed but when I break the residuals down into the levels of each category (the residuals of the predictions for each country) then only two of the three countries have normally distributed residuals. Does this mean that the assumption of normally distributed residuals has been broken? Or is it okay since the overall residuals of the model are normal?

After performing the F -test, it is common to carry out some "post-hoc" analysis of the group means. In this case, the first two group means differ by 4 units, the first and third group means differ by 5 units, and the second and third group means differ by only 1 unit. The standard error of each of these differences is / 6 + / 6 = {\displaystyle {\sqrt {/6+/6}}=} . Thus the first group is strongly different from the other groups, as the mean difference is more times the standard error, so we can be highly confident that the population mean of the first group differs from the population means of the other groups. However, there is no evidence that the second and third groups have different population means from each other, as their mean difference of one unit is comparable to the standard error.

Would it ever be the case that the significance tests of the regression coefficients would come out non-significant when the overall F-test did come out significant? What if, for example, you had a factor with three levels, A, B, and C, with means 3, 5, and 4. If C is the reference level, could it be the case in the regression model that neither the coefficient comparing A to C nor the coefficient comparing B to C would be significantly different from 0, but that the F-statistic would be significant due to the difference between A and B?